The use of IAcM to identify stationarity of the generalized STAR models

A new approach of identifying stationarity of the space-time processes through the Invers of Autocovariance Matrix (IAcM) is proposed. In particular, we consider the first order Generalized Space Time Autoregressive (GSTAR(1;1)) model. This model is considered to be more representative model in space-time modeling due to its realistic assumption on the uniqueness of spatial location. We are exploring the behavior of the IAcM on behalf of the process stationarity. The stationary condition is a must for GSTAR process to be able to apply in space-time modeling. We obtain that the IAcM may be stated as the function of autoregressive parameters and weight spatial. For the confirmation we carry out numerical analysis for various autoregressive parameter matrices and weight matrices. Through some simulations, we illustrate how significant the autoregressive parameters and weight spatial matrices influence the behavior of the IAcM.